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arXiv · 2302.02891

Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces

Eric W. Hester·Geoffrey M. Vasil
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Abstract

We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and collate useful vector calculus identities for these coordinates. These results and provided code enable consistent accounting of geometric effects in the derivation of boundary layer asymptotics for a wide range of physical systems.

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Eric W. Hester, Geoffrey M. Vasil. 2023-02-06. Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces. https://doi.org/10.1098/rspa.2023.0080

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